Solar Position and Intensity
NREL's Solar Position and Intensity (SOLPOS 2.0) C function calculates the apparent solar position and intensity (theoretical maximum solar energy) based on date, time, and location on Earth.
SOLPOS includes three C codes:
- solpos.c – The actual code that computes the sun's intensity and position in the sky
- solpos00.h – The header file that must be included in the code that calls "solpos.c"
- stest00.c – A test code that exercises "solpos.c"
By accessing these files, you agree to abide by the NREL data disclaimer. This software has been tested on a variety of platforms, but it is not guaranteed to work on yours. It is provided here as a convenience
Documentation
This documentation provides an overview of the software functionality. The sample program stest00.c provides additional information by example on how the function is set up and called from an application program. That program serves as the only tutorial for the use of S_solpos.
The module contains three functions:
- S_solpos – Performs calculations
- S_init – Initializes S_solpos
- S_decode – Decodes the return value from S_solpos.
To obtain references for the algorithms, see the references section below. Comments in the source code specify references for each function.
| S_solpos | (computes solar position and intensity from time and place) INPUTS: (via posdata struct defined in solpos00.h) year, daynum, hour, minute, second, latitude, longitude, timezone, interval OPTIONAL: (via posdata struct) month, day, press, temp, tilt, aspect, function OUTPUTS: EVERY variable in the struct posdata (defined in solpos00.h) |
| S_init | (optional initialization for all input parameters in the posdata struct) INPUTS: struct posdata* OUTPUTS: struct posdata* Initializes the required S_solpos INPUTS above to out-of-bounds conditions, forcing the user to supply the parameters; initializes the OPTIONAL S_solpos inputs above to nominal values. See listing below for default values provided by S_init. |
| S_decode | (optional utility for decoding the S_solpos return code) INPUTS: long int S_solpos return value, struct posdata* OUTOUTS: Text to stderr |
Alphabetical List of Common Variables
The I/O column contains a letter code:
I: INPUT variable
O: OUTPUT variable
T: TRANSITIONAL variable used in the algorithm of interest only to the solar radiation modelers.
The FUNCTION column indicates which sub-function within solpos must be switched on using the "function" parameter to calculate the target output variable. All function codes are defined in the solpos00.h file. The default S_ALL mask calculates all output variables. Multiple function masks may be ORed to create a composite function switch. For example, (S_TST | S_SBCF) will force the calculation of the shadow band correction factor as well as all variables required for S_TST (true solar time). Specifying only the functions necessary for required output variables might allow solpos to execute more quickly.
The S_DOY mask works as a toggle between the input date represented as a day of year number (daynum) and an input date represented by month and day of month. To set the switch (to use daynum input), the mask is ORed with the function variable; to clear the switch (to use month and day input), the mask is inverted and ANDed.
For example:
pdat->function |= S_DOY /* (sets daynum input) */
pdat->function &= ~S_DOY /* (sets month and day input) */
Whichever date form is used, S_solpos will calculate and return the variables(s) of the other form. See the sample program stest00.c for other examples.
| VARIABLE | I/O | Function | Description |
|---|---|---|---|
| /**** INTEGERS ****/ | |||
| int day | I/O: | S_DOY | Day of month (May 27 = 27, etc.) solpos will CALCULATE this by default or will optionally require it as input depending on the setting of the S_DOY function switch. |
| int daynum | I/O: | S_DOY | Day number (day of year; Feb 1 = 32 ) solpos REQUIRES this by default, but will optionally calculate it from year, month, and day depending on the setting of the S_DOY function switch. |
| int function | I: | Bit-oriented switch to choose function) for desired output. |
|
| int hour | I: | Hour of day, 0 — 24. (Time 24:00:00 is treated internally as time 00:00:00 of the following day.) |
|
| int interval | I: | Interval of a measurement period in seconds. Forces solpos to use the time and date from the interval midpoint. The INPUT time (hour, minute, and second) is assumed to be the END of the measurement interval. |
|
| int minute | I: | Minute of hour, 0 - 59. | |
| int month | I/O: | S_DOY | Month number (Jan = 1, Feb = 2, etc.) solpos will CALCULATE this by default or will optionally require it as input depending on the setting of the S_DOY function switch. |
| int second | I: | Second of minute, 0 - 59. | |
| int year | I: | 4-digit year (2-digit years NOT allowed) | |
| /**** FLOATS ****/ | |||
| float amass | O: | S_AMASS | Relative optical airmass |
| float ampress | O: | S_AMASS | Pressure-corrected airmass |
| float aspect | I: | Azimuth of panel surface (direction it faces) N=0, E=90, S=180, W=270, DEFAULT = 180 |
|
| float azim | O: | S_SOLAZM | Solar azimuth angle: N=0, E=90, S=180,W=270 |
| float cosinc | O: | S_TILT | Cosine of solar incidence angle on panel |
| float coszen | O: | S_REFRAC | Cosine of refraction corrected solar zenith angle |
| float dayang | T: | S_GEOM | Day angle (daynum*360/year-length) degrees |
| float declin | T: | S_GEOM | Declination--zenith angle of solar noon at equator, degrees NORTH |
| float eclong | T: | S_GEOM | Ecliptic longitude, degrees |
| float ecobli | T: | S_GEOM | Obliquity of ecliptic |
| float ectime | T: | S_GEOM | Time of ecliptic calculations |
| float elevetr | O: | S_REFRAC | Solar elevation, no atmospheric correction (= ETR) |
| float elevref | O: | S_REFRAC | Solar elevation angle, degrees from horizon, refracted |
| float eqntim | T: | S_TST | Equation of time (TST - LMT), minutes |
| float erv | T: | S_GEOM | Earth radius vector(multiplied to solar constant) |
| float etr | O: | S_ETR | Extraterrestrial (top-of-atmosphere) W/sq m global horizontal solar irradiance |
| float etrn | O: | S_ETR | Extraterrestrial (top-of-atmosphere) W/sq m direct normal solar irradiance |
| float etrtilt | O: | S_TILT | Extraterrestrial (top-of-atmosphere) W/sq m global irradiance on a tilted surface |
| float gmst | T: | S_GEOM | Greenwich mean sidereal time, hours |
| float hrang | T: | S_GEOM | Hour angle--hour of sun from solar noon degrees WEST |
| float julday | T: | S_GEOM | Julian Day of 1 JAN 2000 minusn 2,400,000 days (in order to regain single precision) |
| float latitude | I: | Latitude, degrees north (south negative) | |
| float longitude | I: | Longitude, degrees east (west negative) | |
| float lmst | T: | S_GEOM | Local mean sidereal time, degrees |
| float mnanom | T: | S_GEOM | Mean anomaly, degrees |
| float mnlong | T: | S_GEOM | Mean longitude, degrees |
| float rascen | T: | S_GEOM | Right ascension, degrees |
| float press | I: | Surface pressure, millibars, used for refraction correction and ampress |
|
| float prime | O: | S_PRIME | Factor that normalizes Kt, Kn, etc. |
| float sbcf | O: | S_SBCF | Shadow-band correction factor |
| float sbwid | I: | Shadow-band width (cm) | |
| float sbrad | I: | Shadow-band radius (cm) | |
| float sbsky | I: | Shadow-band sky facto | |
| float solcon | I: | Solar constant (NREL uses 1367 W/sq m) | |
| float ssha | T: | S_SRHA | Sunset(/rise) hour angle, degrees |
| float sretr | O: | S_SRSS | Sunrise time, minutes from midnight, local, WITHOUT refraction |
| float ssetr | O: | S_SRSS | Sunset time, minutes from midnight, local, WITHOUT refraction |
| float temp | I: | Ambient dry-bulb temperature, degrees C, used for refraction correction |
|
| float tilt | I: | Degrees tilt from horizontal of panel | |
| float timezone | I: | Time zone, east (west negative)., USA: Mountain = -7, Central = -6, etc. |
|
| float tst | T: | S_TST | True solar time, minutes from midnight |
| floattstfix | T: | S_TST | True solar time - local standard time |
| float unprime | O: | S_PRIME | Factor that denormalizes Kt', Kn', etc. |
| float utime | T: | S_GEOM | Universal (Greenwich) standard time |
| float zenetr | T: | S_ZENETR | Solar zenith angle, no atmospheric correction (= ETR) |
| float zenref | O: | S_REFRAC | Solar zenith angle, deg. from zenith, refracted. |
All functions require the input parameters for time, date, latitude, longitude, time zone, and measurement interval. Some functions may require additional input parameters. The table below indicates with an "X" which, if any, additional input parameters are required for each function. After determining the output variables you require from the above list, make note of the required functions, and then determine the required inputs from the below table.
| Function | Required Inputs | |||||||
|---|---|---|---|---|---|---|---|---|
| solcon | press | sbwid | sbrad | sbsky | temp | tilt | aspect | |
| S_AMASS | -- | X | -- | -- | -- | X | -- | -- |
| S_DOY | -- | -- | -- | -- | -- | -- | -- | -- |
| S_ETR | X | X | -- | -- | -- | X | -- | -- |
| S_GEOM | -- | -- | -- | -- | -- | -- | -- | -- |
| S_REFRAC | -- | X | -- | -- | -- | X | -- | -- |
| S_PRIME | -- | X | -- | -- | -- | X | -- | -- |
| S_SOLAZM | -- | -- | -- | -- | -- | -- | -- | -- |
| S_SRSS | -- | -- | -- | -- | -- | -- | -- | -- |
| S_SSHA | -- | -- | -- | -- | -- | -- | -- | -- |
| S_SBCF | -- | -- | X | X | X | -- | -- | -- |
| S_TILT | X | X | -- | -- | -- | X | X | X |
| S_TST | -- | -- | -- | -- | -- | -- | -- | -- |
| S_ZENETR | -- | -- | -- | -- | -- | -- | -- | -- |
The S_init function provides nominal values for the above inputs. The values are listed below. (Note that time and location variables are initialized out of bounds to force the user to provide valid inputs.)
| day | = | -99 | /* undefined */ |
| daynum | = | -999 | /* undefined */ |
| hour | = | -99 | /* undefined */ |
| minute | = | -99 | /* undefined */ |
| month | = | -99 | /* undefined */ |
| second | = | -99 | /* undefined */ |
| year | = | -99 | /* undefined */ |
| interval | = | 0 | /* instantaneous */ |
| aspect | = | 180.0 | /* south */ |
| latitude | = | -99.0 | /* undefined */ |
| longitude | = | -999.0 | /* undefined */ |
| press | = | 1013.0 | /* standard pressure */ |
| solcon | = | 1367.0 | /* NREL uses this */ |
| temp | = | 15.0 | /* Temperature of the standard atmosphere */ |
| tilt | = | 0.0 | /* horizontal */ |
| timezone | = | -99.0 | /* undefined */ |
| sbwid | = | 7.6 | /* Eppley shadowband */ |
| sbrad | = | 31.7 | /* Eppley shadowband */ |
| sbsky | = | 0.04 | /* Eppley shadowband */ |
| function | = | S_ALL | /* calculate ALL output parameters */ |
Certain conditions exist during which some of the output variables are undefined or cannot be calculated. In these cases, the variables are returned with flag values indicating such. In other cases, the variables may return a realistic, though invalid, value. These variables and the flag values or invalid conditions are listed below.
| amass | -1.0 at zenetr angles greater than 93.0 degrees | |
| ampress | -1.0 at zenetr angles greater than 93.0 degrees< | |
| azim | invalid at zenetr angle 0.0 or latitude +/-90.0 or at night | |
| elevetr | limited to —9 degrees at night | |
| etr | 0.0 at night | |
| etrn | 0.0 at night | |
| etrtilt | 0.0 when cosinc is less than 0 | |
| prime | invalid at zenetr angles greater than 93.0 degrees | |
| sretr | +/- 2999.0 during periods of 24 hour sunup or sundown | |
| ssetr | +/- 2999.0 during periods of 24 hour sunup or sundown | |
| ssha | invalid at the North and South Poles | |
| unprime | invalid at zenetr angles greater than 93.0 degrees | |
| zenetr | limited to 99.0 degrees at night |
S_solpos returns a long integer error code. Each bit position in the long int represents an error in the range of a particular input parameter. The S_decode function in solpos.c examines the return code for errors and can be used as is or as a template for building an application-specific function.
The bit positions for each error are defined in solpos00.h and are listed below. (Bit positions are from least significant to most significant.)
| /* | Code | Bit | Parameter | Range | ||
| =============== | === | =================== | ========= | */ | ||
| enum | {S_YEAR_ERROR, | /* | 0 | year | 1950 - 2050 | */ |
| S_MONTH_ERROR, | /* | 1 | month | 1 - 12 | */ | |
| S_DAY_ERROR, | /* | 2 | day-of-month | 1 - 31 | */ | |
| S_DOY_ERROR, | /* | 3 | day-of-year | 1 - 366 | */ | |
| S_HOUR_ERROR, | /* | 4 | hour | 0 - 24 | */ | |
| S_MINUTE_ERROR, | /* | 5 | minute | 0 - 59 | */ | |
| S_SECOND_ERROR, | /* | 6 | second | 0 - 59 | */ | |
| S_TZONE_ERROR, | /* | 7 | time zone | -12 - 12 | */ | |
| S_INTRVL_ERROR, | /* | 8 | interval (seconds) | 0 - 28800 | */ | |
| S_LAT_ERROR, | /* | 9 | latitude | -90 - 90 | */ | |
| S_LON_ERROR, | /* | 10 | longitude | -180 - 180 | */ | |
| S_TEMP_ERROR, | /* | 11 | temperature (deg. C) | -100 - 100 | */ | |
| S_PRESS_ERROR, | /* | 12 | pressure (millibars) | 0 - 2000 | */ | |
| S_TILT_ERROR, | /* | 13 | tilt | -90 - 90 | */ | |
| S_ASPECT_ERROR, | /* | 14 | aspect | -360 - 360 | */ | |
| S_SBWID_ERROR, | /* | 15 | shadow band width (cm) | 1 - 100 | */ | |
| S_SBRAD_ERROR, | /* | 16 | shadow band radius (cm) | 1 - 100 | */ | |
| S_SBSKY_ERROR}; | /* | 17 | shadow band sky factor | -1 - 1 | */ |
References
Astronomical Solar Position
Michalsky, J. 1988. The Astronomical Almanac's algorithm for approximate solar position
(1950-2050). Solar Energy 40 (3), 227-235.
Michalsky, J. 1988. ERRATA: The astronomical almanac's algorithm for approximate solar position (1950-2050). Solar Energy 41 (1), 113.
Distance from Sun to Earth
Spencer, J. W. 1971. Fourier series representation of the position of the sun. Search 2 (5), 172.
NOTE: This paper gives solar position algorithms as well, but the Michalsky/Almanac
algorithm above is more accurate.
Atmospheric Refraction Correction
Zimmerman, John C. 1981. Sun-pointing programs and their accuracy. SAND81-0761, Experimental Systems Operation Division 4721, Sandia National Laboratories,
Albuquerque, NM.
Shadow Band Correction Factor
Drummond, A. J. 1956. A contribution to absolute pyrheliometry. Q. J. R. Meteorol.2 Soc. 82, 481-493.
Relative Optical Air Mass
Kasten, F. and Young, A. 1989. Revised optical air mass tables and approximation
formula. Applied Optics 28 (22), 4735-4738.
Renormalization of KT (“PRIME”)
Perez, R., P. Ineichen, Seals, R., & Zelenka, A. 1990. Making full use of the clearness
index for parameterizing hourly insolation conditions. Solar Energy 45 (2), 111-114.
Solar Position Relative to Earth
Iqbal, M. 1983. An Introduction to Solar Radiation. Academic Press, NY.
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